Investigating the development process of secondary mathematics teachers' mathematical pedagogical content knowledge: Lesson study model

Knowledge of teaching and learning mathematics has recently turned out to be among hot topics in the studies in mathematics education. However, when considered the thought that teaching and learning mathematics are though subjects, teaching mathematics and its components has come to the forefront. It can be seen when seeking facilitating aspects of teaching mathematics that lesson study model remains an affirmative one. By taking the points mentioned into consideration, it is aimed in the present study to perform the application of lesson study model in the classroom, aimed at improving the teaching knowledge of secondary school mathematics teachers, and to observe the improvements among the teachers during the process. In the scope of the study, among the components of Mathematical Pedagogical Content Knowledge; mathematical content knowledge, knowledge of student, lesson organization and presentation knowledge are emphasised on. The lesson study model has been devoted to the acquirements associated with the area measurement topics in the 6th grade geometry and measurement sub-learning field. The study was conducted including four mathematics teachers working at two different state secondary schools in the city centre of Erzurum province in 2016-2017 academic years. In the study of the lesson study model's effects on Mathematical Pedagogical Content Knowledge of teachers, self-evaluation written opinion form, mathematics content knowledge test, semi-structured interview, observation, lesson plans, diaries and field notes were used as data collection tools. In addition, applied lessons and planning and discussion meetings with the teachers were camera - recorded. This study is an example of the case study of qualitative research methods. Descriptive and content analysis techniques were used in the analysis of the data obtained in the study. Theoretical framework developed by van Es (2011) was employed in order to interpret the awareness level of the teachers after the teaching process. It was determined as the result of the study that the lesson study model contributes to the development of teaching knowledge in the field measurement of secondary school mathematics teachers. Studies conducted during the lesson study model process were determined to affect positively cases of the teachers' knowledge of students, where teachers have difficulty determining and explaining the difficult learning situations of the students. In addition, it was found that teachers make positive contributions to their skills in the categories like preparing plans for the course organization and presentation knowledge, choosing activities, benefiting from concrete materials, ensuring active participation of students in the classroom, introducing mathematical thinking, teaching methods, techniques and strategies. However, lesson study model fell short in the mathematical expressions of concepts taking place in teachers' area measurements. In addition, it was observed that since the studies conducted during the lesson study model supported the professional development of the teachers, students raised awareness about mathematical thinking. Accordingly, in order to apply the lesson study model at schools, teachers may be trained about the subject at work during their seminar periods. Following such trainings, with the supports of experts, group teachers can meet and plan, implement and perform reflective debates on lesson study model in each academic term.